Hello.
Project-> Options-> Version Info (Android 4.4.4) set No TitleBar
In the Object Inspector for the two forms of the application set FullScreen = true.
When start the application, everything is OK with the hide status bar.
On the main form, click on the button with ShowMessage and the status bar climbs and then hides. It looks ugly.

In my application there will be several forms. Now it is clear that the call (e.g.Form2->Show()) of any form will result that the status bar will pop up.
Conclusion:
It is not possible to create application in FMX with several forms if you want to hide the status bar.
It is very sad.
My application shows the menu on the tablet in the restaurant and visitors do not need to see the status bar.

In my application there will be several forms. Now it is clear that the call (e.g.Form2->Show()) of any form will result that the status bar will pop up.
Conclusion:
It is not possible to create application in FMX with several forms if you want to hide the status bar.
It is very sad.
My application shows the menu on the tablet in the restaurant and visitors do not need to see the status bar.

Instead of using separate forms, you could put each 'page' in frame and show/hide the frames as needed. You can create the frames as needed, so the application will load faster.
-Scott

In my application there will be several forms. Now it is clear that the call (e.g.Form2->Show()) of any form will result that the status bar will pop up.
Conclusion:
It is not possible to create application in FMX with several forms if you want to hide the status bar.
It is very sad.
My application shows the menu on the tablet in the restaurant and visitors do not need to see the status bar.

Instead of using separate forms, you could put each 'page' in frame and show/hide the frames as needed. You can create the frames as needed, so the application will load faster.
-Scott

Yes, I have to completely remake the interface. It is a pity that I spent a lot of time.
Another additional question:
Is this the standard android behavior that we can not use the mode to hide status bar when we use Form.Show/ShowMessage or is it a problem FMX?
Thank you all for your advice!